P-wave Superconductor Junctions Research Articles

Shot noise and tunneling magnetoresistance in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions

We investigate the transport properties in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions within the Blonder–Tinkham–Klapwijk formalism by solving the Dirac–Bogoliubov-de Gennes equation. The results show that the conductance and the shot noise strongly depend on the p-wave superconducting pair potentials and the magnetic configurations of the ferromagnetic regions. The simultaneous diminution of the conductance and enhancement of the shot noise can be achieved with the increase of the antiferromagnetic exchange field strength. The conductance and the shot noise can be effectively modulated by the external electric field and the ferromagnetic exchange field strength, and the corresponding switch effects are also achieved. The tunneling magnetoresistance (TMR) outside the subgap energy interval is always larger than the one obtained in the subgap energy interval. When the antiferromagnetic exchange field strength is large enough, a larger TMR can be obtained by tuning the external electric field.

Charge transport in silicene-based ferromagnetic p-wave superconductor junctions

Using Blonder-Tinkham-Klapwijk (BTK) formalism we studied the transport properties in silicene-based normal/ferromagnetic p-wave superconductor (N/FpS) junctions. Our study shows that the amplitude of the normalized conductance strongly depends on the pairing symmetry in superconductor such as px, py and px+ipy-wave symmetries, the applied electric field (EZ) and the exchange field (h) in FpS. In N/FpxS-silicene junctions the zero-bias conductance peak is obtained due to the Andreev bound states. When the electric field and magnetic field are parallel, called P configuration, there is one conductance dip (CD) for the voltage eV=lEz−λSO with λSO the spin obit coupling term and 2l the distance between two sublattices in the buckled silicene. In the anti-parallel (AP) configuration there is one CD at eV=lEz−λSO for 0<lEz−λSO<h and for lEz−λSO≥h there are two CDs at eV=h and eV=lEz−λSO, respectively. A sudden transition of conductance from zero to maximum (henceforth referred to as“switching of conductance”) at eV=lEz−λSO occurs in both N/FpyS-silicene junction and N/Fpx+ipyS-silicene junction. In N/FpyS-silicene junction the Andreev resonant peak appears at eV=h for lEz−λSO−h=0.1Δ00 in the AP case, where Δ00 is the zero temperature gap of the FpS. In N/Fpx+ipyS-silicene junctions the maximum value of the conductance appears at eV=Δ00−h in P junction while in AP junction at eV=Δ00+h.

Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical p-wave states

We study the Josephson effect in spin-singlet superconductor/helical p-wave superconductor junctions with a ferromagnetic barrier using the quasiclassical Green function method. It is found that both sin ϕ-type and cos ϕ-type current-phase relations always exist, irrespective of the gap symmetries in superconductors. The indispensable condition for the sin ϕ-type and cos ϕ-type current is that the magnetization must have a component parallel to the crystallographic a- or b-axis, which is distinct from the case of the p-wave superconductor described by a d-vector with a uniform direction. The relation between the condition and the symmetries of the gap functions is analysed. We investigate in detail the symmetries and the sign reversal of the Josephson current when the magnetization is rotated.

Quantum point contact conductance in normal metal/insulator/ metal/ [formula omitted] mixed wave superconductor junctions

The tunneling conductance in a normal metal/insulator/metal/ d x 2 − y 2 + i d x y mixed wave superconductor (N/I/N/ d x 2 − y 2 + i d x y ) junction is calculated, where the N/I/N region is a quantum wire. It is found in the single-mode case that the magnitude of the tunneling conductance near zero voltage is enhanced due to the Andreev bound state by quasiparticles with perpendicular and horizontal injection, and the zero-bias conductance varies with L ( L is the distance from insulating layer to the interface of N/ d x 2 − y 2 + i d x y mixed wave superconductor). Splitting of the zero-bias conductance peak appears in the quantum point contact tunneling spectra for an N/I/N/ d x 2 − y 2 + i d x y junction, and several subgap peaks can split at the same time. On increasing both L and the magnitude ratio of the two components for the d x 2 − y 2 + i d x y mixed wave, the subgap resonances exhibit an alternately high and low behavior inside the energy gap. These results are different from those in d-wave and p-wave superconductor junctions.

Tunneling conductance in quantum wire/insulator/dx2-y2 + idxy mixed wave superconductor junctions

Using the extended Blonder–Tinkham–Klapwijk (BTK) theory, this paper calculates the tunnelling conductance in quantum wire/insulator/dx2-y2 + idxy mixed wave superconductor (q/I/dx2-y2 + idxy) junctions. That is different from the case in d- and p-wave superconductor junctions. When the angle α between a-axis of the dx2-y2 wave superconductor and the interface normal is π/4, there follows a rather distinctive tunnelling conductance. The zero-bias conductance peak (ZBCP) may or may not appear in the tunnelling conductance. Both the interface potential z and the quasi-particle lifetime factor ΓT are smaller, there is no ZBCP. Otherwise, the ZBCP will appear. The position of bias conductance peak (BCP) depends strongly on the amplitude ratio of two components for dx2-y2 + idxy mixed wave. The low and narrow ZBCP may coexist with the BCP in the tunnelling conductance. Using those features in the tunnelling conductance of q/I/dx2-y2 + idxy junctions, it can distinguish dx2-y2 + idxy mixed wave superconductor from d- and p-wave one.

Dependence of Josephson Current on Orientational Angle in Diffusive p-Wave Superconductor Junctions

We calculate Josephson current in p-wave superconductor (P)/diffusive normal metal (DN)/insulator/diffusive normal metal/p-wave superconductor junctions, using quasi-classical Green’s function theory. We study the dependence of the critical current on the orientational angle at various temperatures. We find that the critical current in these junctions are proportional to cos αcos β. Here, α and β are angles between the direction perpendicular to the interfaces, located between the DN and P, and the crystal axis of left and right P respectively.

Manifestation of the odd-frequency spin-triplet pairing state in diffusive ferromagnet/superconductor junctions

Using the quasiclassical Green's function formalism, we study the influence of the odd-frequency spin-triplet superconductivity on the local density of states (LDOS) in a diffusive ferromagnet (DF) attached to a superconductor. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli's principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of these states, the pairing state in DF is studied. Particular attention is paid to the study of spin-singlet s-wave and spin-triplet p-wave superconductors as the examples of ESE and ETO superconductors. For spin-singlet case the magnitude of the OTE component of the pair amplitude is enhanced with the increase of the exchange field in DF. When the OTE component is dominant at low energy, the resulting LDOS in DF has a zero energy peak (ZEP). On the other hand, in DF / spin-triplet p-wave superconductor junctions LDOS has a ZEP in the absence of the exchange field, where only the OTE paring state exists. With the increase of the exchange field, the ESE component of the pair amplitude induced in DF is enhanced. Then, the resulting LDOS has a ZEP splitting. We demonstrate that the appearance of the dominant OTE component of the pair amplitude is the physical reason of the emergence of the ZEP of LDOS.

Josephson current between p-wave superconductors

Josephson current in p-wave superconductor/diffusive normal metal (DN)/p-wave superconductor junctions is calculated by solving the Usadel equation under the Nazarov’s boundary condition extended to unconventional superconductors by changing the heights of the insulating barriers at the interfaces, the magnitudes of the resistance in DN, and the angles between the normal to the interface and the lobe directions of p-wave pair potentials. It is shown that the magnitude of the Josephson current strongly depends on the lobe directions of the p-wave pair potentials and the resulting magnitude of the Josephson current is large compared to that in the s-wave superconducting junctions due to the formation of the resonant states peculiar to p-wave superconductors.

Anomalous Josephson Effect inp-Wave Dirty Junctions

The Josephson effect in p-wave superconductor/diffusive normal metal/p-wave superconductor junctions is studied theoretically. Amplitudes of Josephson currents are several orders of magnitude larger than those in s-wave junctions. Current-phase (J-phi) relations in low temperatures are close to those in ballistic junctions such as J proportional to sin(phi/2) and J proportional to phi even in the presence of random impurity potentials. A cooperative effect between the midgap Andreev resonant states and the proximity effect causes such anomalous properties and is a character of the spin-triplet superconductor junctions.

Tunneling conductance anomalies in normal metal/triplet superconductor junction

In the framework of the Blonder-Tinkham-Klapwijk model，we calculate the differential tunneling conductance in normal metal / insulator / normal metal/triplet p-wave superconductor junctions which is studied theoretically as a function of the bias voltage. The results show that there are zero-bias conductance peak, zero-bias conductance dip, double-minimum structures and oscillation components of the differential conductance in the spectra for p-wave superconductor junctions. It can be seen that additional current steps appear in the I-V relationship. The existence of such structures in the conductance spectrum may serve as an evidence that the pairing of Sr2RuO4 has p-wave symmetry.

Theory of thermal and charge transport in diffusive normal metal/superconductor junctions

Thermal and charge transport in the diffusive normal metal(DN) / insulator / $s$-, $d$- and p-wave superconductor junctions are studied for various situations, where we have used the Usadel equation with Nazarov's generalized boundary condition. Thermal and electrical conductance of the junction and the Lorentz ratio are calculated by varying the magnitudes of the resistance, the Thouless energy and the magnetic scattering rate in DN, the transparency of the insulating barrier, and the angle between the normal to the interface and the crystal axis of d-wave superconductors or the angle between the normal to the interface and the lobe direction of the p-wave pair potential. New general expression is derived for the calculation of the thermal conductance. It is demonstrated that the proximity effect doesn't influence the thermal conductance while the mid gap Andreev resonant states suppress it. We have also discussed a possibility of distinguishing pairing symmetries based on the dependencies of the electrical and thermal conductance on temperatures.

Tunneling Conductance in Normal Metal/Insulator/TripletSuperconductor Junction

Tunneling conductance in normal metal/insulator/triplet superconductorjunctions is studied theoretically as a function of the bias voltage at zerotemperature and finite temperature. The results show there are zero-biasconductance peak, zero-bias conductance dip and double-minimum structures inthe spectra for p-wave superconductor junctions. The existence of suchstructures in the conductance spectrum can be taken as evidence that thepairing symmetry of Sr2RuO4 is p-wave symmetry.

Temperature dependence of spin-polarized transport in ferromagnet/unconventional superconductor junctions

Tunneling conductance in ferromagnet/unconventional superconductor junctions is studied theoretically as a function of temperature and spin polarization in ferromagnets. In d-wave superconductor junctions, a zero-energy Andreev bound state drastically affects the temperature dependence of the zero-bias conductance (ZBC). In p-wave superconductor junctions, numerical results show various temperature dependences of the ZBC depending on the direction of the magnetic moment in ferromagnets and the pairing symmetry in superconductors such as ${p}_{x}\ensuremath{-},$ ${p}_{y}\ensuremath{-},$ and ${p}_{x}{+ip}_{y}$-wave symmetries. The last one is a candidate for the pairing symmetry of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ From these characteristic features in the conductance, we may obtain information about the degree of spin polarization in ferromagnets and the direction of the d vector in spin-triplet superconductors.